Using an Approximate Chi‐Square Statistic to Test the Number of Dimensions Underlying the Responses to a Set of Items
Authors:
- Marc E. GessaroliMGMarc E. Gessaroli
- André F. De ChamplainACAndré F. De Champlain
- 1 June 1996
- journal article
- Published by Wiley in Journal of Educational Measurement
- Vol. 33 (2) , 157-179
Abstract
An approximate χ2 statistic based on McDonald's (1967) nonlinear factor analytic representation of item response theory was proposed and investigated with simulated data. The results were compared with Stout's T statistic (Nandakumar & Stout, 1993; Stout, 1987). Unidimensional and two‐dimensional item response data were simulated under varying levels of sample size, test length, test reliability, and dimension dominance. The approximate χ2 statistic had good control over Type I errors when unidimensional data were generated and displayed very good power in identifying the two‐dimensional data. The performance of the approximate χ2 was at least as good as Stout's T statistic in all conditions and was better than Stout's T statistic with smaller sample sizes and shorter tests. Further implications regarding the potential use of nonlinear factor analysis and the approximate χ2 in addressing current measurement issues are discussed.Keywords
This publication has 32 references indexed in Scilit:
- Assessing Dimensionality of a Set of Item Responses‐Comparison of Different ApproachesJournal of Educational Measurement, 1994
- Refinements of Stout's Procedure for Assessing Latent Trait UnidimensionalityJournal of Educational Statistics, 1993
- The Effect of Test Length and IRT Model on the Distribution and Stability of Three Appropriateness IndexesApplied Psychological Measurement, 1992
- DIMTEST: A Fortran Program for Assessing Dimensionality of Binary Item ResponsesApplied Psychological Measurement, 1992
- Traditional Dimensionality Versus Essential DimensionalityJournal of Educational Measurement, 1991
- Three Approaches to Determining the Dimensionality of Binary ItemsApplied Psychological Measurement, 1991
- The Difficulty of Test Items That Measure More Than One AbilityApplied Psychological Measurement, 1985
- Latent Structure and Item Sampling Models for TestingAnnual Review of Psychology, 1985
- Dimensionality, bias, independence and measurement scale problems in latent trait test score modelsBritish Journal of Mathematical and Statistical Psychology, 1980
- TESTS OF SIGNIFICANCE IN FACTOR ANALYSISBritish Journal of Statistical Psychology, 1950